What is the mean of the following comparable sales prices: $285,000, $295,000, $305,000, $275,000, and $290,000?
Correct Answer
C) $290,000
Why this is correct: The mean (average) is calculated by summing all values and dividing by the count. Step 1: Sum = $285,000 + $295,000 + $305,000 + $275,000 + $290,000 = $1,450,000. Step 2: Divide by the number of values (5): $1,450,000 / 5 = $290,000. Why the other choices are wrong: '$285,000' is the lowest value in the set, not the mean. '$305,000' is the highest value in the set. '$295,000' is one of the values and is close to the mean, but it is not the calculated average. Exam tip: On the exam, double-check your addition and division. A quick way to estimate: the numbers center around $290,000, confirming the calculated mean is reasonable.
Why This Is the Correct Answer
Option A ($290,000) is correct because it represents the accurate arithmetic mean of the five comparable sales prices. The calculation involves adding all five values: $285,000 + $295,000 + $305,000 + $275,000 + $290,000 = $1,450,000, then dividing by the number of comparables (5) to get $290,000. This systematic approach to calculating the mean ensures that all data points are equally weighted in determining the central value. The mean provides a reliable measure of central tendency that appraisers use as a starting point for further analysis and adjustments.
Why the Other Options Are Wrong
Option A: $285,000
Option A ($285,000) is incorrect as it represents the second-lowest individual comparable sale price, not the calculated mean. This value appears in the original dataset but is not the result of proper mean calculation. Choosing this option suggests confusion between individual data points and the computed average, which is a fundamental error in statistical analysis.
Option B: $305,000
Option B ($305,000) is incorrect because it represents the highest individual comparable sale price rather than the calculated mean of all five values. This is the maximum value in the dataset, which some might mistakenly identify as representative of the group. Confusing the highest value with the mean demonstrates a lack of understanding of basic statistical measures and their distinct purposes in data analysis.
Option D: $295,000
Option D ($295,000) is incorrect because it represents one of the individual comparable sales prices rather than the calculated mean of all five values. This appears to be the second-highest value in the dataset, which might be confused with the mean by someone who didn't perform the actual calculation. Selecting an individual data point instead of calculating the average is a common error that occurs when candidates rush through mathematical problems.
ADD-DIVIDE Method
Remember 'ADD all values, DIVIDE by count' - use your fingers to count the number of comparables while adding them up, then divide by the number of fingers you used.
How to use: When you see a mean calculation question, immediately count the number of values on your fingers, add all the dollar amounts together, then divide by the finger count to get your answer.
Exam Tip
Always double-check your addition when calculating means - write down each value clearly and add them twice to avoid arithmetic errors, as these questions often include answer choices that represent common calculation mistakes.
Common Mistakes to Avoid
- -Adding the values incorrectly due to rushing
- -Forgetting to divide by the total number of comparables
- -Selecting one of the individual comparable prices instead of calculating the mean
Concept Deep Dive
Analysis
This question tests the fundamental statistical concept of calculating the arithmetic mean (average) of comparable sales data, which is a cornerstone of the sales comparison approach in real estate appraisal. The mean provides appraisers with a central tendency measure that helps establish a baseline value when analyzing multiple comparable properties. Understanding how to calculate and interpret the mean is essential for making informed adjustments and arriving at accurate property valuations. This basic statistical skill is frequently applied in appraisal practice and is a foundational concept that appears regularly on licensing exams.
Background Knowledge
The arithmetic mean is calculated by summing all values in a dataset and dividing by the number of observations, providing a measure of central tendency that equally weights each data point. In real estate appraisal, the mean of comparable sales helps establish a baseline value before making specific adjustments for differences between the subject property and the comparables.
Real-World Application
Appraisers regularly calculate the mean of comparable sales to establish a baseline value range for the subject property, then make individual adjustments for differences in size, condition, location, and other factors to arrive at a final opinion of value.
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